We present a theory of the magnetoplasmons of two-dimensional electron grid (antidot) structures. We develop a variational Wigner-Seitz model to study such periodic electron structures. We derive an analytical solution for the far-infrared (FIR) response, and obtain results in quantitative agreement with experiments. Our work provides not only an explanation for the recently observed FIR anomaly, but also a useful basis for further theoretical studies of collective properties of electron grid (antidot) structures.